Digital interference holographic microscope and methods

ABSTRACT

A simple digital holographic apparatus and method allow reconstruction of three-dimensional objects with a very narrow depth of focus or high axial resolution. A number of holograms are optically generated using different wavelengths spaced at regular intervals. They are recorded, such as on a digital camera, and are reconstructed numerically. Multiwavelength interference of the holograms results in contour planes of very small thickness and wide separation. Objects at different distances from the hologram plane are imaged clearly and independently with complete suppression of the out-of-focus images. The technique is uniquely available only in digital holography and has applications in holographic microscopy.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to provisional application 60/156,253,filed Sep. 27, 1999.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to microscopic imaging, and, moreparticularly, to holographic microscopy for reconstruction ofthree-dimensional objects and optical tomographic imaging forselectively imaging cross sections of an object.

2. Description of Related Art

Imaging of microscopic objects is an essential art, not only in biologyand medicine, but also in many other fields of science and technology,including materials science, microelectronics engineering, and geology.Modern microscopy takes advantage of discoveries on the interactionbetween electromagnetic and other fields with material objects, and hastaken on numerous incarnations, such as electron transmission andscanning microscopes, the scanning tunneling microscope, the atomicforce microscope, and the laser scanning confocal microscope (Isenberg,1998).

Rapid progress in electronic detection and control, digital imaging,image processing, and numerical computation has been crucial inadvancing modern microscopy. By equipping an optical microscope with adigital or video camera, a range of image processing and patternrecognition techniques can be applied for automated image acquisitionand analysis (Herman and Lemasters, 1993).

One particular aspect of microscopic imaging of interest is the axialresolution or depth of focus. In a conventional optical microscope, thelateral resolution can be a fraction of a micrometer, whereas the axialresolution is typically several micrometers or more. This leads to tworelated difficulties: One is that the axial position cannot bedetermined with better than a few-micrometer accuracy; another is thatthe overlap of images from object planes several micrometers apart leadsto blurring and degradation of images. Usually the only remedy availableis physical sectioning of the specimen into thin slices, which precludesa large range of materials from being studied.

A remarkable solution to these problems was the scanning confocalmicroscope, developed just over a decade ago (Sheppard and Shotton,1997). by illumination of a single object point and placement of adetection aperture at the image point, the detector behind the apertureregisters a light signal originating only from the object point. A two-or three-dimensional image is constructed by pixel-by-pixel scanning ofthe object volume. The whole of the resulting image is sharply in focus,and the size of the acquirable image is limited only by the stabilityand speed of the scanning and processing system.

Another important optical scanning system is the near-field opticalscanning microscope, where the light signal is probed by a highlytapered optical fiber at a distance only a fraction of an opticalwavelength from the sample surface, thereby circumventing thediffraction limit of resolution in far-field imaging. However, theapplication of this technique in imaging wet and delicate biologicalsamples has been limited because of the requirement to maintain aconstant surface-probe distance with accuracy and stability. It is moresuitable for the study of macromolecular structures, as with otherrelated scanning devices that utilize electron tunneling, atomic force,and other subtle interactions on the atomic and molecular level.

Holography was originally invented in an attempt to improve theresolution of a microscope (Hariharan, 1996). Both the amplitude andphase information of the light wave are recorded in a hologram by theinterference of an object wave that is to be imaged with a referencewave of simple structure such as a plane or spherical wave. Theinterference pattern is recorded in a variety of media, most commonly ona photographic plate. The object wave is reconstructed as one of thediffraction patterns when a replica of the reference wave is incident onthe photographic plate. The resulting image is an exact copy of thelight wave that originally emanated from the object, and thus has theproperty of perspective vision.

Because the holographic image retains the phase as well as the amplitudeinformation, a variety of interference experiments can be performed, andthis is the basis of many interferometric applications in metrology. Itis possible accurately to measure deformation and other variations of anobject at a submicrometer level because of advances in digital imagingand numerical computing technology. Thus it is often advantageous toreplace steps of the holographic procedure with digital processes(Yaraslavskii and Merzlyakov, 1980).

In computer-generated holograms (CGH) the interference pattern iscomputed from a mathematical definition of a virtual object andreference (Trester, 1996). The patter is output to a hard-copy device,and laser illumination results in an optical hologram image.

On the other hand, in computer-reconstructed holograms (CRH), theoptical interference pattern of a real object and reference is recordedusing an electronic or digital camera (Schnars and Jüptner, 1996). Thepattern is digitized and stored in a computer, and the holographic imageis recreated on the computer by numerical calculation.

In either CGH or CRH, the numerical calculation basically imitates theoptical diffraction process as the light wave propagates from the objectto the hologram plane or from the hologram plane to the image plane.This can be accomplished using Fresnel diffraction theory or Huygenswavelet theory (Kreis et al, 1997). An important aspect of research inthis area is in attempts to minimize the computational load using, forexample, segmentation of holograms and horizontal-only parallax(Karnaukhov et al., 1998; Yang et al., 1998a,b).

Digital holography alleviates the need for wet chemical processing of aphotographic plate, although at some expense of resolution. However,once the amplitude and phase (i.e., all the essential information) ofthe light wave are recorded numerically, one can easily subject thesedata to a variety of manipulations, and so digital holography offerscapabilities not available in conventional holography. For example, thephase information of the light wave is available directly from thenumerical reconstruction and greatly simplifies interferometricdeformation analysis (Seebacher et al., 1998; Kreis et al, 1998; Cucheet al, 1999; Brown and Pryputniewicz, 1998).

Holography can be applied to microscopy in two alternative ways. In one,a hologram of a microscopic object is taken directly, and the hologramis inspected using a microscope; in the other, a microscope is usedfirst to magnify the object image, and the hologram is taken of thatimage. Holographic microscopy has been particularly useful in particleanalysis, where a particle count has to be obtained in a volume of fluid(Vikram, 1992). With a conventional microscope, the constant motion ofparticles into and out of the focal plane makes it difficult toascertain an accurate count as the focal plane is scanned across theentire sample volume. A holographic micrograph freezes thethree-dimensional field, and a particle count can proceed by focusing onsuccessive planes.

Holographic microscopy in three-dimensional imaging applications hasbeen limited partly because of the inherent scale distortion of anoptical microscope image of a volume object. The axial magnificationgoes as the square of the lateral magnification, so that the twodirections magnify with different ratios, and the lateral magnificationalso depends on the axial distance. When the hologram is viewed byfocusing on a plane, the same problem of out-of-focus image blurring ispresent as in an optical microscope (Zhang and Yamaguchi, 1998; Poon etal., 1995).

Application of digital holography in microscopy holds potentiallyattractive benefits (Schilling et al., 1997). In principle, once theamplitude and phase information of the object image is numericallystored, it can be manipulated by image processing techniques for removalof distortion and out-of-focus blurring. Interference measurements canyield subwavelength resolution of features, and particle analysis andfeature recognition can be automated with greater efficiency.

Another imaging technique, tomography, has been utilized in biomedicaland materials sciences (Robb, 1997), with optical tomography most usefulin microscopic imaging because of the short wavelength and limitedpenetration depth of most biological surfaces. For example, laserconfocal microscopy (Sheppard and Shotton, 1997) uses aperturing of boththe illuminated sample volume and the detector aperture, therebyrejecting all scattered light other than from the focal volume. Opticalcoherence tomography (Huang et al., 1991; Morgner et al., 2000) is atime-of-flight measurement technique, using ultrashort laser pulses or acontinuous-wave laser of very short coherence time. In both of thesemethods the signal is detected one pixel at a time, and thethree-dimensional image is reconstructed by scanning thethree-dimensions pixel by pixel. Although microscanning using piezoactuators is an important technique, being able to obtain image framesat a time would have technical advantages.

By recording the phase as well as the intensity of light waves,holography allows reconstruction of the image of 3D objects, and givesrise to many metrological and optical processing techniques (Hariharan,1996). It is now possible to replace portions of the holographicprocedure with electronic processes (Yaroslavsky and Eden, 1996). Forexample, in digital holography the hologram is imaged on a CCD array,replacing photographic plates of conventional holography. The digitallyconverted hologram is stored in a computer, and its diffraction isnumerically calculated to generate simulation of optical images.

With digital holography, real-time processing of the image is possible,and the phase information of the reconstructed field is readilyavailable in numerical form, greatly simplifying metrologicalapplications (Cuche et al., 1998). Previously limiting memory and speedfactors have improved (Trester, 1996; Piestun et al., 1997). On theother hand, for the purpose of tomographic imaging, although thehologram produces a 3D image of the optical field, this does not byitself yield the tomographic distance information to the object surfacepoints, other than by focusing and defocusing of the object points,which is really a subjective decision (Poon et al., 1995; Zhang andYamaguchi, 1998a). The distance information can be obtained intime-of-flight-type measurements, or it can be determined by countingthe number of wavelengths or some multiples of it, which is the basis ofvarious interference techniques.

One technique is the interference of two holograms recorded at twodifferent wavelengths, resulting in a contour interferogram with theaxial distance between the contour planes inversely proportional to thedifferences in wavelengths. In digital holography, it is possible toextend the process to recording and reconstruction of many hologramswithout introducing any wavelength mismatch or crosstalk. If a number ofregularly spaced wavelengths are used for recording and reconstruction,then the peaks of the cosine-squared intensity variation oftwo-wavelength interference become sharper and narrower, as when anumber of cosines with regularly spaced frequencies are added.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a simple digitalholographic method and apparatus for reconstructing three-dimensionalobjects with a very narrow depth of focus or axial resolution.

It is another object to provide such a method and apparatus that affordssubmicrometer resolution in both the lateral and the longitudinaldirections.

It is a further object to provide such a method and apparatus whereinthe blurring and degrading of images due to out-of-focus object planesare substantially completely suppressed.

It is an additional object to provide such a method and apparatus thatcarries out an interference process in numerical virtual space.

Another object is to provide such a method and apparatus wherein theobtained optical sectioned images can be reassembled into athree-dimensional digital model that can be further manipulated forspecific applications, such as correction of scale distortion, arbitrarysection and cutaway views, and automatic feature enhancement andidentification.

A further object is to provide a method and apparatus for imaging athree-dimensional object having a diffuse surface.

An additional object is to provide such a method and apparatus forgenerating a three-dimensional numerical model of the imaged surfacestructure.

These and other objects are achieved by the present invention, a firstembodiment of which comprises an apparatus and method for imagingthree-dimensional microscopic volume objects with digital holographicmicroscopy.

As is known in the art, interference of two holograms recorded at twodifferent wavelengths results in a contour interferogram, with the axialdistance between the contour planes inversely proportional to thedifference in wavelengths. In CRH, unlike in conventional holography,the reconstruction of each hologram is done using the correspondingwavelength that was actually used in the recording process. Therefore,it is possible to extend the process to recording and reconstruction ofmany holograms without introducing any wavelength mismatch. If a numberof regularly spaced wavelengths are used for recording andreconstruction, then the peaks of cosine-squared intensity variation oftwo-wavelength interference becomes sharper and narrower, as when anumber of cosines with regularly spaced frequencies are added.

The present invention addresses a practical problem in microscopy, wherethe axial magnification goes as the square of the transversemagnification. Even at moderate magnification, it is difficult to bringthe entire microscopic object into focus, while the out-of-focusportions of the object image contribute to blurring and noise of thefocal plane image. Confocal scanning microscopy (CSM) addresses thisproblem very successfully (Sheppard and Shotton, 1997), although therequirement of stability and precision of lengthy mechanical scanningcan be quite significant.

A hologram has depth perception and axial resolution, but determinationof axial location in particle analysis, for example, depends only on thefocusing of the image as the depth is varied (Zhang and Yamaguchi,1998b), and out-of-focus blurring presents the same problem as inmicroscopy.

The present invention involves no mechanical motion, and wavelengthscanning and multiple exposure can be electronically automated for speedand stability. Furthermore, many of the holographic interferometric andoptical processing techniques can be applied to the resulting images forvarious applications.

The principle of wavefront reconstruction by holography is well known.The electric field E₀ arriving from an object interferes with a planar,or other simply structured, write reference wave E_(r), resulting in anintensity pattern of:I˜|E _(r) +E ₀|² =|E _(r)|² +|E ₀|² +E _(r) *E ₀ +E _(r) E ₀*which is recorded in some manner. In CRH one may subtract the zero-orderterms |E_(r)|² and |E₀|², and the remaining terms give rise to theholographic twin images. For simplicity, one neglects the effect of theconjugate image and considers the third term in the above equation only,and also lets the reference wave be planar and incident perpendicular tothe hologram plane, so that E_(r)˜1. In reconstruction, if one also usesE_(r) as the read reference wave, then the diffracted wave isproportional to E₀, a replica of the original object wave (or itsconjugate E₀*).

Now consider an object point P located at (x₀, y₀, z₀), which emits aHuygens spherical wavelet proportional to A(P)exp(ikr_(P)) measured atan arbitrary point Q=(x, y, z), where r_(p)=|r_(P)−r_(Q) is the distancebetween P and Q, and the 1/r dependence of the amplitude is neglected.The wave propagates in the general z direction. The factor A(P)represents the field amplitude and phase at the object point. For anextended object, the field at Q is proportional to the above waveletfield integrated over all the points on the object:E _(k)(Q)˜_(∫) _(P) d ³ r _(P) A(P)exp(ikr _(P))This is the field that is present in the vicinity of the object undermonochromatic illumination, and this is also the field reconstructed byholography. The factor exp(ikr_(P)) represents the propagation anddiffraction of the object wave. Now suppose a number of copies of theelectric field are generated by varying the wave numbers k (orwavelengths λ), all other conditions of object and illuminationremaining the same. Then the resultant field at Q is:

${\left. {E(Q)} \right.\sim{\sum\limits_{k}\;{\int_{P}\ {{\mathbb{d}{{}_{}^{}{}_{}^{}}}{A(P)}{\exp\left( {{\mathbb{i}}\;{kr}_{P}} \right)}}}}} = {\int_{P}\ {{\mathbb{d}{{}_{}^{}{}_{}^{}}}{A(P)}{\sum\limits_{k}\;{\left. {\exp\left( {{\mathbb{i}}\;{kr}_{P}} \right)} \right.\sim{\int_{P}\ {{\mathbb{d}{{}_{}^{}{}_{}^{}}}{A(P)}{\left. {\delta\left( {r_{P} - r_{Q}} \right)} \right.\sim{A(Q)}}}}}}}}$That is, for a large enough number of wave numbers k, the resultantfield is proportional to the field at the object, and nonzero only atobject points. In practice, if one uses a finite number N of wavelengthsat regular intervals of Δλ (with corresponding intervals of frequenciesΔf), then the object image A(P) repeats itself at axial distancesΛ=λ²/Δλ=c/Δf with an axial resolution of δ=Λ/N. By using appropriatevalues of Δλ and N, the contour plane distance Λ can be matched to theaxial extent of the object and δ to the desired level of axialresolution. Note that for a given level of axial resolution δ, therequired range of wavelengths N Δλ is the same as the spectral width oflow-coherence or short-pulse lasers in optical coherence tomography.

Optical sectioning microscopy by wavelength-scanning digitalinterference holography (WS-DIH) proceeds as follows. A microscopicobject is illuminated by a laser, and a microscope lens forms a realmagnified image of the object. Light from this intermediate image and areference beam interferes at a CCD array surface, which is recordeddigitally into a computer. The laser wavelength is stepped by Δλ for thenext exposure, and the process is repeated N times, which completes therecording process. The axial scale of the object determines thenecessary wavelength step Δλ. Using the example of a 10-μm-radius sphereand 50×lateral magnification, the longitudinal extent of theintermediate image is 20 μm×50²=50 mm, which sets the minimum for thecontour plane distance A. Using 600-nm light, the required frequencystep is Δf=c Δλ/λ²=6 GHz. To obtain effective axial resolution of, say,1 μm=20 μm/20, one needs to take 20 hologram images while scanning thelaser frequency up to 120 GHz=4 cm⁻¹. These parameters are easily withinrange of many laser systems, including dye lasers and semiconductorlasers. Note that the frequency step Δf is inversely proportional to theobject axial scale Λ.

The set of N digitally stored holograms represents the completeinformation required for computational reconstruction of thethree-dimensional image. For each hologram, after subtraction ofzero-order intensities, a diffraction theoretical formula is applied tocompute the light wave field of the image. Repeat the computation of Nholographic images, and they are added together for digitalinterference. The resultant image is an intensity distribution patternthat corresponds to three-dimensional map of scattering centers of theobject, such as the boundary surfaces, internal structures, and otherpoints of irregularities in absorption or dispersion of light.

The result can be displayed as two-dimensional cross sections of theobject at an arbitrary distance from the hologram plane. With the set ofnumerical representation of the images, further manipulation andprocessing is possible. For example, the microscopic image distortion,including the unequal lateral-axial magnifications and the axialdependence of the lateral magnification, can be processed out byapplying corrective scale factors. The corrected cross sections can thenbe reassembled into a three-dimensional computer model with naturalaspect ratios. The three-dimensional computer model is then availablefor application-specific manipulations such as viewpoint changing,cutaway views, feature enhancement, and others.

The system of the present invention takes advantage of the unique powerof digital holography to provide a simple and versatile mode ofthree-dimensional microscope imaging. One may put this concept inperspective in terms of its potential advantages over other imagingmodes and of possible difficulties that may arise.

-   -   The lateral resolution should be as good as conventional optical        microscopy, except that the present system is a coherent imaging        system, and so one needs to exercise care with speckle noise and        other interference effects. On the other hand, the multiple        exposure of the scheme of the present invention tends to have a        signal-averaging effect. Studies seem to indicate such an        enhancement of image quality.    -   The axial or longitudinal resolution is excellent in comparison        with conventional optical microscopy. Scanning confocal        microscopy was developed to address the problem of axial        resolution in conventional optical microscopy. The axial        resolution of a confocal system is determined mainly by the        focal depth of the illuminated spot, to ˜0.5 μm. With WS-DIH, a        comparable axial resolution may be expected or even exceeded.        Digital holography has been used to demonstrate ˜λ/10 or ˜50 nm        vertical resolution in the inspection of a microelectronics        circuit.    -   The wavelength scanning system of the present invention has no        mechanical moving components. In principle, the amount of voxel        (volume element) data generated by WS-DIH is the same as in SCM:        M_(x)×M_(y)×N, where the Ms are the number of pixels in the x        and y directions and N is the number of z sections. In SCM, the        system has to raster scan each plane pixel by pixel and then        repeat the process for N planes. The requirement of mechanical        accuracy and stability can be substantial and entails an        elaborate feedback control system. On the other hand, the        present system acquires a single whole plane of data in one        shot, and in most laser systems tuning and scanning of the        gigahertz range is electronically controllable, providing        efficiency, stability, and accuracy. With present CCD        technology, however, the bottleneck may occur at the image        transfer rate between the CCD array and the computer memory.    -   The system of the present invention is a holographic system, and        as such, the complete amplitude and phase information of the        light field is available. One can take advantage of this        information that is not available in other imaging systems, for        applications in interferometry and holographic image processing.

The features that characterize the invention, both as to organizationand method of operation, together with further objects and advantagesthereof, will be better understood from the following description usedin conjunction with the accompanying drawing. It is to be expresslyunderstood that the drawing is for the purpose of illustration anddescription and is not intended as a definition of the limits of theinvention. These and other objects attained, and advantages offered, bythe present invention will become more fully apparent as the descriptionthat now follows is read in conjunction with the accompanying drawing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an apparatus for multiwavelength digitalholography.

FIGS. 2A–2E are reconstructions of an image of a single object (OBJ1)using a single wavelength: FIG. 2A, reference beam; FIG. 2B, object beamat the screen; FIG. 2C, interference between the reference and theobject; FIG. 2D, intensity patterns of FIGS. 2A and 2B subtracted fromFIG. 2C; FIG. 2E, numerically reconstructed image at z_(i)=z₀=149 cm.

FIGS. 3A–C are reconstructions of images of two objects (OBJ1 and OBJ2)using a single wavelength: FIG. 3A, interference pattern betweenreference and object, minus zero-order terms; numerically reconstructedimages: FIG. 3B, at z_(i)=z_(o1)=149 cm; and FIG. 3C, atz_(i)−z_(o2)−165 cm.

FIGS. 4A–4D are reconstructed image patterns as functions of imagedistance. The horizontal axis is z_(i) in cm, and the vertical axis, inmm, is a slice of the reconstructed image along the dotted line shown inFIG. 3C: FIG. 4A, a single wavelength or frequency; FIG. 4B, combinationof two holograms at relative frequencies, 0.0 and 1.0 GHz; FIG. 4C, tworelative frequencies, 0.0 and 2.0 GHz; FIG. 4D, three relativefrequencies, 0.0, 1.0, and 2.0 GHz.

FIGS. 5A and 5B are reconstructed images with two objects using elevenholograms: FIG. 5A, at z_(i)=z_(o1)=149 cm; FIG. 5B, at z_(i)=z_(o2)=165cm.

FIG. 6 is a schematic of an apparatus for digital interferenceholography.

FIG. 7A is a direct camera image of a damselfly under laserillumination; FIG. 7B is a numerically reconstructed image from onehologram; FIG. 7C is an image accumulated from 20 holograms.

FIGS. 8A–8C are digitally recorded optical fields: FIG. 8A, a hologram;FIG. 8B, an object, OO*; FIG. 8C, a reference, RR*.

FIG. 9 is an animation of a z-y cross section of the three-dimensionalreconstructed field at x=−1.3 mm, as 20 3D arrays are added in digitalinterference holography.

FIG. 10A are x-y cross sections of the accumulated array at variousaxial distances z; FIG. 10B are z-y cross sections of the accumulatedarray at various x values starting from the left end of the head, x=1.84mm, to near the middle of the head, x=0.52 mm.

FIG. 11 is an animated three-dimensional reconstruction of the insect'silluminated surface.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A description of the preferred embodiments of the present invention willnow be presented with reference to FIGS. 1–11.

The apparatus 10 of the present invention is depicted in FIG. 1. A ringdye laser 12 provides a 595.0-nm laser field of ˜50-mW power with alinewidth of ˜50 MHz. The laser beam is expanded with a microscopeobjective 14 to 20 mm diameter and divided into three parts using beamsplitters 16,18. One of these provides the planar reference beam 20,while the other two 22,24 constitute the object beam. The objectconsists of two transparency targets attached to the back-reflectingmirrors (M) 26,28 in separate optical arms, in order to avoidobstruction of one object by the other in the same optical path. Onetarget 30 (OBJ1) is a checkerboard pattern with 2.5-mm grid size, andthe other target 32 (OBJ2) is a transparent letter “A” that fits insidean opaque square of side 13 mm.

The object 22,24 and reference 20 beams are combined in a Michaelsoninterferometer arrangement and sent to a translucent Mylar screen S 34.The object distances to the screen are approximately 149 and 167 cm. Theinterference pattern on the screen is imaged, for example, by digitalcamera 36, such as a Kodak DC120, through another lens L2 38 foradjustment of focus and magnification. The exemplary camera 36 has960×1280 pixels with 10×10 μm² pixel size. The calculations presentedhere use 256×256 pixel images of screen area 13×13 mm, so that theeffective pixel resolution on the screen is 51 μm, although this is notintended to be limiting. The corresponding minimum distance for theobject is then 1.1 m, in order to accommodate the interference betweenrays emanating from the two ends of a 13-mm object. For each hologram,the reference beam and the object beam are imaged separately, so thatthese images can be subtracted before reconstruction and the resultingimages do not contain zero-order terms. It is not attempted to eliminatethe conjugate image. The process is repeated a plurality of times, hereup to 11 laser frequencies spaced 1.0 GHz apart, to achieve a desiredaxial period Λ of the resultant hologram images, here 30 cm, and adesired axial resolution δ, here 3.0 cm.

For reconstruction of images, a software package, for example, a MatLabprogram, encodes the Fresnel diffraction, which is equivalent to Eq. (2)with appropriate approximations (Goodman, 1968):

E(x,y;z)=exp[(ik/2z)(x ² +y ²)]F{E ₀(x ₀ ,y ₀)S(x ₀ ,y ₀ ;z)}[k _(x) ,k_(y)]

whereS(x,y;z)=−(ik/z)exp[ikz+(ik/2z)(x ² +y ²)]k_(x)=kx/z, k_(y)=ky/z, and F{f}[k] represents a Fourier transform fwith respect to the variable k.

FIGS. 2A–2D illustrate the input images of the reference (R, FIG. 2A),the object (O, using OBJ1, FIG. 2B), the interference hologram betweenthe two (H, FIG. 2C), and the subtracted image E=H−R−O (FIG. 2D). Theholographic image in FIG. 2E of the single object is reconstructed atz_(i)=149 cm, and shows typical resolution and quality of thereconstructed images (z_(o) and z_(i) are object and image distances,respectively, measured from the screen). The remaining fringe patterninside the squares is due to the out-of-focus twin image.

FIG. 3A shows the hologram with both objects OBJ1 and OBJ2 on, aftersubtraction of reference and object images. The images are reconstructednear the two object distances (FIG. 3B) z_(i1)=149 cm and (FIG. 3C)z_(i2)=165 cm. The two images are substantially indistinguishable andcontain images of both objects, although it is possible to discerndifferences in the sharpness of focus between the two images. The axialresolution determined by focal sharpness is at least ˜15 cm, as can beseen in FIG. 4A, where the vertical axis is a slice of the reconstructedimage along the dotted vertical line of FIG. 3C and the horizontal axisis the image distance z_(i) from 140 to 190 cm.

In FIG. 4B two holograms with frequency separation of 1.0 GHz arecombined, showing the expected cosine-squared modulation with a periodof 30 cm, whereas in FIG. 4C, two frequencies 2.0 GHz apart are combinedand the period is now 15 cm. In FIG. 4D, three relative frequencies of0.0, 1.0, and 2.0 GHz are combined, and the narrowing of interferencemaxima is evident (cf. FIGS. 4B and 4D). Also note that the images ofOBJ1 and OBJ2 focus at different z_(i) locations: The three bright areasnear z_(i)=150 cm (and also at 180 cm) are the three bright squares ofOBJ1's checkerboard, while the bright patch near y=−3.0 mm, z_(i)=165 cmcorresponds to the lower left corner of OBJ2's letter “A.” Carrying thisprocess further, eleven holograms with frequencies 0.0, 1.0, 2.0, . . ., 10.0 GHz are combined in FIG. 4E, which results in an axial resolutionof ˜3 cm, as expected.

The images at two distances are shown in FIG. 5A for z_(i1)=149 cm andz_(i2)=165 cm. Now each of the images contains only one of OBJ1 or OBJ2,and the out-of-focus images are substantially suppressed.

The invention thus demonstrates the use of multiwavelength interferenceof computer-reconstructed holograms for high axial resolution ofthree-dimensional images. The apparatus is very simple and amenable toelectronic automation without mechanical moving parts. Even withless-than-optimal laser and imaging systems, the theoretically predictedaxial resolution is easily achieved. The main source of imperfection inFIGS. 4A–4D, for example, was the mode hop and drift of thenonstabilized laser frequency. Another embodiment may include, forexample, the use of a compact diode laser, direct transfer of an imageto a CCD array surface, and automation of the multiple exposure forspeed and stability. The technique can be applied to both microscopicand telescopic imaging for cross-sectional imaging of objects of variousscales. The cross-sectional images can then be recombined withappropriate scaling for the removal of distortion, resulting in asynthesis of three-dimensional models that can be subjected to furtheranalysis and manipulation.

In a second embodiment of the present invention, a holographic apparatus40 (FIG. 6) comprises a laser, for example, a ring dye laser 41. Aportion, here 50 mW, of the laser's output is passed through a firstneutral density filter 42 and is expanded to a predetermined diameter,here 10 mm, with a beam expander and spatial filter 43.

The beam 90 is apertured 44 to a desired diameter, here 5 mm, anddirected to a first beam splitter 45. A first portion 91 of the splitbeam passes through a second neutral density filter 46 and becomes thereference beam 92. A second portion 93 of the split beam is directed tothe object 80, here a damselfly specimen, shown under laser illuminationin FIG. 6A, wherein the eyes, mouthpiece, and front several legs arevisible.

The scattered light 94 from the object 80 is combined with the referencebeam 92 at a second beam splitter 47 to form an interference beam 95,which then passes through a magnifying lens 48 to image the opticalimage at the camera's 49 focal plane 50 onto infinity. The camera 49,for example, a digital camera (such as model DC290, manufactured byKodak, Rochester, N.Y.), is focused at infinity, so that it records amagnified image of the optical intensity at the plane S 50. Theobject-to-hologram distance 51 here is 195 mm. The object beam 94preferably should be apertured so that it only illuminates the area ofthe object 80 that is to be imaged; otherwise, spurious scattering canseriously degrade the contrast and resolution of the reconstructedimage.

At a given laser wavelength, three images are recorded: a hologram ofthe object and reference interference (HH*=|O+R|², FIG. 8A), the objectonly (OO*, FIG. 8B), and the reference only (RR*, FIG. 8C). The laserwavelength is then stepped, starting from λ₀=601.7 nm at Δλ=0.154-nmintervals for N=10 steps, so that the expected axial range is Λ=2.35 mmand the axial resolution is δ=0.12 mm.

The digitally recorded images are transferred to a computer 52, wheresoftware means 53, for example, a set of MatLab® scripts, are used fornumerical reconstruction. A desired area, here 4.8×4.8 mm, of the imageis interpolated to a 512×512 pixel matrix. In an alternate embodiment, aCCD array is used instead of the camera 49, wherein the imagemagnification and interpolation steps are not performed.

The object and reference frames are then numerically subtracted from thehologram frame, HH*-OO*-RR*, before applying Fresnel diffraction, toeliminate zero-order diffraction. A clean holographic image is thenobtained even at 0° offset between the object and reference beams. It isbelieved that this leaves conjugate images RO* and R*O, but one of theseis substantially completely out of focus and does not appear tointerfere with the process of the present invention. The holographicimage field is then calculated as above.

The numerical reconstruction and digital interference proceeds bystarting from a 512×512 pixel, 4.8×4.8 mm digital hologram (withzero-order subtraction). The Fresnel diffraction patterns are calculatedat N+1=21 z values, z=Z₁+mδ, where Z₁=195 mm is the original objectdistance 51 and m=−10, −9, . . . , 9, 10. This results in a 3D array of512×512×21 pixels and a 4.8×4.8×2.35 mm volume, representing theholographic optical field variation in this volume.

This process is repeated for 20 sets of triple digitally recorded imagesat 20 different wavelengths. At this point, the field patterns in theindividual 3D arrays show little variation along a few millimeters ofthe z direction. Then the 20 3D arrays are numerically superposed byadding the arrays element wise, resulting in the accumulated field arrayof the same size. This new array then has a field distribution thatrepresents the 3D object structure, as described previously. Inpractice, owing to the laser's frequency fluctuation and imprecision ofthe wavelength intervals, there is a random phase variation among the 20calculated field arrays. This may be corrected by introducing a globalphase factor into each of the 3D arrays before carrying out thesummation.

FIG. 7B is an example of a 2D holographic image reconstructed from asingle hologram at Z₁=195 mm. Imaging of diffuse scattering objects,such as the biological specimen of this exemplary illustration, usingcoherent illumination gives rise to speckle noise, causing degradationof contrast and resolution. This can be reduced somewhat by optimizingthe illumination aperture and the overall stability of the opticalsystem.

The effect of digital interference is illustrated in FIG. 9. Theanimation frames show a 2.35×4.8 mm z-y cross section at x=−1.3 mm, asthe holographic field arrays are added on top of each other from 1 to20. When N=1, the z variation is due to a small diffraction of thefield, but at N=2 the field exhibits cosine variation in the zdirection, with a different phase origin depending upon theobject-to-surface distance. As further arrays are added, the cosinepattern becomes similar to ∂-function spikes in the z direction. Whenall 20 field arrays are accumulated, only one z value has a significantintensity above noise for each object surface pixel.

FIGS. 10A and 10B show cross-sectional tomographic views of theaccumulated field array, with FIG. 10A showing x-y cross sections as theaxial distance z is varied from the front tip of the mouthpiece to theback of the eyes, over a distance of 2.35 mm. FIG. 10B shows z-y crosssections as the x value is varied from 1.84 to 0.52 mm, or from the edgeof the insect's left eye to the middle of the face.

The contrast of these images is numerically enhanced by taking thelogarithm and applying thresholding to the calculated field arrays. Thustomographic imaging by wavelength-scanning digital interference isclearly demonstrated. The accumulation of N holographic field arrays hasan additional benefit of averaging out the coherent speckle noise.

FIG. 7C is obtained by starting from the accumulated array and summingover the z direction, yielding a 2D image of the object 80. Theresulting image quality approaches that of the photographic image ofFIG. 7A, and the speckle noise is substantially completely removed.Further, each object surface element is imaged in focus regardless ofthe depth of focus of the optical system. This feature is especiallybeneficial in an embodiment applied to microscopic imaging with a largenumerical aperture.

An animated 3D reconstruction of the object's illuminated surface ismade by plotting the brightest volume elements in 3D perspective (FIG.11). As the azimuthal angle rotates, the two eyes and mouthpiece arerecognizable as being the most prominent features. Two or three frontlegs are also visible, although there appear to be ghost images present.

This embodiment has demonstrated three-dimensional imaging of a smallbiological specimen using wavelength-scanning digital interferenceholography. Cross-sectional images of the object are generated withclear focus and suppression of coherent speckle noise. The resolutionsachieved are ˜100 μm in the axial direction and tens of micrometers inthe lateral direction, as defined by the optical system and computercapacity of the present embodiment, and are thus not intended aslimitations. With a semitransparent microscopic object, full tomographicimaging is possible.

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1. A method for imaging a three-dimensional object comprising the stepsof: (a) illuminating an object with radiation at a wavelength to form areflected image beam; (b) providing a reference beam comprising thewavelength; (c) recording an interference pattern between the referencebeam and the image beam; repeating steps (a)–(c) at a succession ofdifferent wavelengths separated by a predetermined wavelength step;computing a holographic image from the interference pattern for eachwavelength; adding the holographic images together to form an intensitydistribution pattern; extracting out a series of two-dimensionalcross-sectional images from the intensity distribution pattern;correcting microscopic image distortion in the cross-sectional images;and reassembling the cross-sectional images into a three-dimensionalmodel of the object.
 2. The method recited in claim 1, wherein theilluminating step comprises illuminating the object with coherentradiation.
 3. The method recited in claim 2, further comprising the stepof expanding the coherent radiation prior to the illuminating step. 4.The method recited in claim 1, wherein the predetermined wavelength stepcomprises a function of an axial scale of the object.
 5. The methodrecited in claim 1, further comprising the step of subtracting azero-order intensity from each computed holographic image prior to theadding step.
 6. A method for imaging a three-dimensional objectcomprising the steps of: (a) illuminating an object with radiation at awavelength to form a reflected image beam; (b) providing a referencebeam comprising the wavelength; (c) recording an interference patternbetween the reference beam and the image beam; (d) recording an image ofthe object only; and (e) recording an image of the reference beam only;repeating steps (a)–(e) at a succession of different wavelengthsseparated by a predetermined wavelength step; computing a holographicimage from the interference pattern for each wavelength; subtracting azero-order intensity from each computed holographic image, wherein thesubtracting step comprises subtracting the object-only andreference-beam-only images from the interference pattern; and adding theholographic images together to form an intensity distribution pattern.7. The method recited in claim 6, wherein the computing step comprisescalculating a holographic image field at each wavelength using a Fresneldiffraction formula.
 8. A method for imaging a three-dimensional objectcomprising the steps of: (a) illuminating an object with radiation at awavelength to form a reflected image beam; (b) providing a referencebeam comprising the wavelength; (c) recording an interference patternbetween the reference beam and the image beam; repeating steps (a)–(c)at a succession of different wavelengths separated by a predeterminedwavelength step; computing a holographic image from the interferencepattern for each wavelength; and adding the holographic images togetherto form an intensity distribution pattern, wherein the object comprisestwo two-dimensional objects positioned different distances from a sourceof the radiation, and further comprising the step of extracting out twotwo-dimensional cross-sectional images from the intensity distributionpattern, each image representative of one of the objects.
 9. The methodrecited in claim 8, wherein the extracting step comprises encoding theFresnel diffraction as a function of a Fourier transform with respect toradiation wavelength.